International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 9, September 2014) 291 Modified RSA Algorithm with CRT & OAEP Bhumi J. Patel 1 , Nitin J. Janwe 2 1,2 Department of Computer Science & Engg., RCERT, Chandrapur, India 442401 Abstract— The most active subjects in the security related communities are the necessary protection against the data thieves. This gives an importance and the value of exchanged data over the Internet or other media types. In many RSA cryptosystems, we usually select a small value for the public key e. This kind of choice can only speed up the encryption operation but do not forget that by this way, the corresponding decryption operation requires more computational time and therefore it costs more because of the larger decryption exponent d. The alternative way that can be taken to overcome this problem is to implement this operation is based on the Chinese Remainder theorem (CRT). This paper deals with implementation of RSA algorithm using Chinese remainder Theorem. To provide extra layer of encryption we will use Optimal Asymmetric Encryption Padding (OAEP) and Variable Radix Number System. Keywords— Encryption, Decryption, RSA Algorithm, CRT, Optimal Asymmetric Encryption Padding, Hash Algorithm . I. INTRODUCTION Cryptography is the science of information security. In today's computer-centric world, cryptography is most often associated with scrambling plaintext (ordinary text, sometimes referred to as clear text) into cipher text (a process called encryption), then back again (known as decryption). As the technology is growing, security is considerable in many applications such as private networks, e-commerce, secure internet access, securing confidential reports at army level etc.. E-business security is an overarching business issues that, based of an analyzed risks, and establishes the threat acceptance and reduction parameters for the safe use of technology. As an overarching issue, e-business security can be thought of as being absolutely fundamental to the effective and efficient use of Information Technology in support of e-business. There are many algorithms that are used to provide the encryption. RSA algorithm is the well known of all the algorithms. It provides a well defined security. The RSA algorithm consists of three different steps i.e., key generation, encryption and decryption. All these three steps depend very much on each other with regards to efficiency and computational costs. RSA algorithm is asymmetric type of cryptosystems also called as public key systems. It has two keys i.e., public key and private key. For encryption e is used as a public key and d is used as a private key also called as secret key for decryption process. The private key is very important as only the key holder can decrypt the cipher texts to the original plaintexts. In many RSA cryptosystems, they usually select a small value for the public key e. This kind of choice can only speed up the encryption operation but do not forget that by this way, the corresponding decryption operation costs more computational time because of the larger decryption exponent d. In order to include RSA cryptosystem efficiently in many protocols, it is desired to devise faster encryption and decryption operations. The alternative way that can be taken to overcome this problem is to implement this operation is based on the Chinese Remainder theorem (CRT). II. EXISTING TECHNIQUE A. RSA Algorithm RSA is an asymmetric cryptographic algorithm. Asymmetric means that there are two different keys. This is also called public key cryptography, because one of them can be given to everyone. The other key must be kept private. It is based on the fact that finding the factors of a integer is hard (the factoring problem). RSA stands for Ron Rivest, Shamir and Adleman, who first publicly described it in 1978. A user of RSA creates and then publishes the product of two large prime numbers, along with an auxiliary value, as their public key. The prime factors must be kept secret. Anyone can use the public key to encrypt a message, but with currently published methods, if the public key is large enough, only someone with knowledge of the prime factors can feasibly decode the message. The RSA scheme is a block cipher in which the plaintext and cipher text are integers between 0 and n-1 for some n. A typical size for n is 1024 bits. That is, n is less than 2 1024 . The scheme makes use of an expression with exponentials. Plaintext is encrypted in blocks, with each block having a binary value less than some number n. That is, the block size must be less than or equal to log2 (n); in practice, the block size is i bits, where 2i < n <2i+1. Encryption and decryption are of the following form, for some plaintext block M and cipher text block C: